All flow sensors that employ the differential thermal anemometry technique suffer from a limited linear range.
Typically, these are thermal flow sensors that operate as shown in FIG. 1. A discrete thermal plug introduced into a liquid filled tube/channel will disperse in both the upstream and downstream directions due to thermal conduction or diffusion, respectively. In the case where a discrete section of the fluid in the tube/channel is continuously heated, a temperature profile similar to Ca in FIG. 1 will develop (i.e., a zero flow condition). The shape of this temperature profile will depend upon the amount of heat added to the fluid and the upstream and downstream temperatures of the liquid. Assuming identical upstream and downstream fluid temperatures, under this zero-flow condition, liquid temperatures measured at P1 and P2 will be equal as thermal diffusion will be equal in both directions. If the liquid in the tube/channel is permitted to flow, the fluid temperatures at P1 and P2 will now also depend upon the rate of liquid flux and the resulting heat convection. As liquid begins to flow past the heated zone, a temperature profile similar to CB in FIG. 1 will develop since, in addition to the symmetrical diffusion of the heat, asymmetrical convection of the heated fluid will occur in the direction of the fluid flow. Therefore, under flowing conditions, fluid temperatures measured at P1 and P2 will be different. Temperature measurements made at P1 and P2 can be sampled, subtracted and amplified electronically in situ to allow a high degree of common-mode noise rejection which will allow discrimination of extremely small upstream and downstream temperature differences.
Although the differential temperature is proportional to flow at low flow rates, at elevated flow rates, this relationship becomes nonlinear. At low flow rates, the temperature of the heater is essentially constant as the convection of heat carried away from the heater due to the flowing liquid is relatively small. A thermal flow sensor operated in this low flow range has essentially a linear response of upstream/downstream ΔT with flow. At higher flow rates, this convective heat removal from the heater becomes non-trivial. If constant power is applied to the heater, its temperature will decrease. As the temperature of the heater decreases, the upstream/downstream temperatures will necessarily converge and the ΔT response to flow rate changes will decrease. At extremely high flow rates, this convection will become so large that an increase in flow rate will actually cause a decrease in ΔT.
It is this phenomenon that limits the effective range of any sensor design based on thermal anemometry. It is not uncommon for flow sensors to be used outside their linear range by using a polynomial function to linearize the raw sensor response. While this is effective, it requires processing of the analog signal and can only extend the flow sensor range to the point where the ΔT response to flow is still measurable and positive. Also, while a flow sensor can be designed appropriately to handle large fluid flows without decreasing the heater temperature, this typically requires a more massive heater with larger surface area to be used. Such a heater would make the sensor unsuitable for measuring low fluid flow rates as its response to flow changes would be very slow.
Accordingly, there is a need for devices and methods that extend the linear range of flow sensing apparatus for both low and high flow applications.